Without differentiating between damage types, a fire burst and an ice ray are functionally equivalent.
Are they? One of them can be used to set things alight. The other can be used to freeze puddles of water.
The difference can be an important part of the fiction without needing a mechanical difference between damage types.
I suspect that's, in practice, differentiating damage types on at least a minimalist level.
Here are two examples that illustrate my point.
In a game of Marvel Heroic RP that I GMed, one of the players played Ice Man (Bobby Drake). That character has the ability Ice Mastery. At one point in our game, the player declared, as an action, that he (ie Bobby) froze the water in the Reflecting Pool near the Washington Monument, so that it could be skated on.
MHRP does not use damage types. The difference between what can be done by creating or manipulating ice/cold, and what can be done by creating or manipulating fire/heat, is a matter of understanding and adjudicating the fiction.
In my group's Prince Valiant game, one of the PCs owns a dagger that has been blessed by St Sigobert (within the context of our game a fictional saint, although John Nephew presumably derived the name from the historical
St Sigeberht). When the PCs witnessed a demon being driven from a possessed bull, in the form of smoke, the PC with the dagger through the demon-smoke to try and destroy it. Prince Valiant does not have a system of damage types - the fact that this was a blessed dagger was a feature of the fiction, not a mechanical property like "+1D holy
I'd argue if it means anything "can set things on fire" is a mechanical difference. Among other things it brings up questions like "How often will that happen? If it happens to a human how long will they burn and what damage will they take?"
dagger". The effect of the dagger on the demon was adjudicated as an element of the fiction.
Why is it important to the fiction?
9 times out of 10 the spellcaster's next questions become matters of mechanics: What things on the target's person did I burn up? When I froze the puddle the target was standing on, does he fall prone?
You seem to be assuming combat scenario involving small-scale skirmishes. Those weren't really what I had in mind.
But even in that context, not everything you are describing is, or has to be, a function of
mechanics. Suppose that I am playing a game in which my PC magician can conjure an ice ray. And suppose it is established that, in the fiction, an enemy is standing in a puddle. Then I might declare an action, "I want to blast the water so it freezes around my enemy's feet, trapping them." Or suppose that is is established that there is a puddle between me and my enemy, and the GM says that the enemy is running towards me. I might declare the action, "I want to blast the water so that it freezes, so that my enemy slips over when they run over the ice."
These are actions that
can be declared if I my magician can conjure an ice ray, and that
cannot be declared if my magician can conjure a fiery blast. In the latter case, though, I can declare actions like "I set the building alight" or "I burn the scroll that my enemy is holding".
Adjudicating these declared actions doesn't depend upon the system having damage types. It just depends upon there being some process for resolving declared actions, that has reference to the established fiction. In the MHRP game that I mentioned, Bobby's player did other freeze-y stuff with cold and ice, that were different from the sorts of things that Pyro might have been able to do in the same circumstances.
I'd argue if it means anything "can set things on fire" is a mechanical difference. Among other things it brings up questions like "How often will that happen? If it happens to a human how long will they burn and what damage will they take?"
Prince Valiant has no mechanical answers to any of those questions. How often will a burning brand set things on fire? That depends on what sorts of actions players whose PCs are wielding burning brands declare, and what sorts of framing or consequences are established by the GM. What happens to a person who is burned by a burning brand? Like all questions of injury and recovery in Prince Valiant, that is for the GM to decide.
In a session of Wuthering Heights that I GMed, the culmination involved one of the PCs - a ghost (as a result of that player's mortal character having died of a heart attack early in the session) - suggesting to the other - a bookshop worker who had suffered a series of emotionally shocking experiences - that he burn the shop down with himself in it. This was resolved using the general system mechanic for killing oneself. It did not require or involve any mechanics about damage type, nature and degree of injury, etc. It's obvious to anyone who is familiar with late Victorian urban design and building fittings that it can be
possible to cause a house fire in which a person dies, especially in a bookshop which contains a large amount of flammable material; and so the relevant question was simply
whether or not the character succeeded in their attempt to do this thing, and as I said that was resolved by applying the relevant general mechanic.
In a session of Classic Traveller, the PCs needed to blast through a significant amount of ice, to get to an alien installation buried beneath the ice. They cut through most of it using their ship's triple beam laser - we (ie the game participants) Googled up and collectively extrapolated from a paper on the use of lasers to cut through ice to reach consensus on how long this would take. The final bits of blasting were done with explosives, and for that a Demolitions check was rolled for the NPC who knew how to handle them, which - as per the mechanics - makes sure that things work as intended and no one inadvertently gets blown up. Again, there was no need to apply any rules for damage or damage types. We had agreement on what was possible - ie that lasers and explosives can blast away ice - and a roll was made simply to check that nothing went wrong in the process.
Now ask those questions of any three people sitting around a table and see what happens. In practice, if fire spells are going to be assumed to do that, either the question will be answered in the printed rules, in house-rules, or in house-rules-in-everything-but-name (i.e. convention). Any of the three are still rules relevant, even if people like to claim that's not what the third case is.
My post that prompted this particular line of discussion was about damage types, and in this post I've talked more generally about mechanics. Now you are talking about
rules.
Bobby Drake's Ice Mastery ability is described in the PC rules - it's a particular case of Elemental Control, and the degree of power is defined in this way,
Elemental Mastery d10 provides citywide control: extinguishing a burning skyscraper; freezing over a city street; bringing down a city’s power grid, while the affected element is described thus, *Ice/Cold: Rapidly decreasing the thermal properties of the environment, producing ice, freezing things *.
That is not a damage type mechanic. It is not a mechanic about how much or how often Ice Man can freeze things. It is a description, in terms of the fiction, of what it is possible for Ice Man to do. The only
mechanic is the d10 - this is the die that Bobby's player adds to their dice pool when trying to find out whether or not Bobby's attempt to freeze something succeeds.
In my experience - of which I've provided some examples in this post - it is possible for there to be agreement among the participants as to what is possible, and for there to be rules that help determine whether or not the possible becomes actual, without the need for the sorts of house rules you describe, and in the absence of damage types or similar sorts of mechanics.
It just seems the cases where it did work halfway well (and I saw some, though admittedly plenty of the opposite) should count as something.
